Direction : Consider the following for the items that follow :  

The roots of the quadratic equation 

a²(b² - c²)x² + b²(c² - a²)x + c²(a² - b²) = 0 are equal (a² ≠ b² ≠ c²).

If $\sqrt{2}$ and $\sqrt{3}$ are roots of the equation $a_0 + a_1 x + a_2 x^2 + a_3 x^3 + x^4 = 0$ where $a_0, a_1, a_2, a_3$ are integers, then which one of the following is correct?